Precise high moment asymptotics for parabolic Anderson model with log-correlated Gaussian field

Yangyang Lyu

Statistics & Probability Letters, 2020, vol. 158, issue C

Abstract: In this paper, we consider the continuous parabolic Anderson model (PAM) driven by a time-independent log-correlated Gaussian field (LGF). We obtain an asymptotic result of Eexp{12∑j,k=1N∫0t∫0tγ(Bj(s)−Bk(r))drds}(N→∞) which is composed of the independent Brownian motions {Bj(s)} and the function γ approximating to a logarithmic potential at 0, such as the covariances of massive free field and Bessel field. Based on the asymptotic result, we get the precise high moment asymptotics for Feynman–Kac formula of the PAM with LGF.

Keywords: Precise high moment asymptotics; Large deviation; Log-correlated Gaussian field; Massive free field; Bessel field (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2019.108662

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